Abstract
We consider a family of deformations describing cylindrical inflations within the context of finite, compressible, isotropic elasticity. We pose the problem of finding the maximal class of materials for which these deformations are possible at equilibrium under surface tractions only. We solve this problem for families of cylindrical inflations whose principal strain invariants have a special dependence on the radius. These families comprise and extend all cases considered by Murphy [2].
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References
M.M. Aron, On a class of plane radial deformations of compressible nonlinearly elastic solids, IMA J. Appl. Math. 52(1995) 289-296.
J.G. Murphy, A familly of solutions describing plane strain cylindrical inflation in finite compressible elasticity, J. Elasticity 45(1996) 1-11.
J.L. Ericksen, Deformations possible in every compressible, perfectly elastic material body, J. Math. Phys. 34(1955) 126-128.
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Martins, L., Duda, F. Maximal Classes of Stored Energies Compatible with Cylindrical Inflations. Journal of Elasticity 53, 189–198 (1998). https://doi.org/10.1023/A:1007528818132
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DOI: https://doi.org/10.1023/A:1007528818132